Limit Location Constraint on Armature Breaks in a Loop Animation
After a few days I have managed to fix it. If anyone comes across the same issue I believe my answer should help.
Again following the tutorial by Max Berends at https://www.youtube.com/watch?v=t1GmLAVeySY
You must have your tracking empty exactly on the pivot point between the lower pump section and the connecting arm.
I recommend using:

Object&gt;SetOrigin&gt;OrigintoGeometry/(Shift+S) to set the origin to the mesh.
At your new origin point, create the new empty.
Once you have an armature from the top point of the arm, go into edit mode for the armature, select the second point and go to Object&gt;SetOrigin&gt;SelectedtoOrigin


I think the discrepancies in location can slowly throw out the animation in this case because of the &quot;TrackTo&quot; constraint, as seen in the video in my question post. Having the empty in the exact location has fixed it.
Hope this can help someone.